24 research outputs found
Quantum Loops in Non-Local Gravity
In this proceedings, I will consider quantum aspects of a non-local,
infinite-derivative scalar field theory - a depiction of a
covariant infinite-derivative, non-local extension of Einstein's general
relativity which has previously been shown to be free from ghosts around the
Minkowski background. The graviton propagator in this theory gets an
exponential suppression making it , thus
providing strong prospects of resolving various classical and quantum
divergences. In particular, I will find that at -loop, the -point
function is still divergent, but once this amplitude is renormalized by adding
appropriate counter terms, the ultraviolet (UV) behavior of all other -loop
diagrams as well as the -loop, -point function remains well under
control. I will go on to discuss how one may be able to generalize our
computations and arguments to arbitrary loops.Comment: Contribution to the Proceedings of the "Corfu 2014" Conference in
Corfu, Greece, September 2014; v2: minor revision
Towards understanding the ultraviolet behavior of quantum loops in infinite-derivative theories of gravity
In this paper we will consider quantum aspects of a non-local,
infinite-derivative scalar field theory - a depiction of a
covariant infinite-derivative, non-local extension of Einstein's general
relativity which has previously been shown to be free from ghosts around the
Minkowski background. The graviton propagator in this theory gets an
exponential suppression making it , thus providing
strong prospects of resolving various classical and quantum divergences. In
particular, we will find that at -loop, the -point function is still
divergent, but once this amplitude is renormalized by adding appropriate
counter terms, the ultraviolet (UV) behavior of all other -loop diagrams as
well as the -loop, -point function remains well under control. We will go
on to discuss how one may be able to generalize our computations and arguments
to arbitrary loops.Comment: 52 pages, 8 figures; v3: Published in Classical and Quantum Gravity;
v4: minor revision
High-energy scatterings in infinite-derivative field theory and ghost-free gravity
In this paper, we will consider scattering diagrams in the context of infinite-derivative theories. First, we examine a finite-order, higher-derivative scalar field theory and find that we cannot eliminate the growth of scattering diagrams for large external momenta. Then, we employ an infinite-derivative scalar toy model and obtain that the external momentum dependence of scattering diagrams is convergent as the external momenta become very large. In order to eliminate the external momentum growth, one has to dress the bare vertices of the scattering diagrams by considering renormalised propagator and vertex loop corrections to the bare vertices. Finally, we investigate scattering diagrams in the context of a scalar toy model which is inspired by a ghost-free and singularity-free infinite-derivative theory of gravity, where we conclude that infinite derivatives can eliminate the external momentum growth of scattering diagrams and make the scattering diagrams convergent in the ultraviolet
The tensorial representation of the distributional stress-energy quadrupole and its dynamics
We investigate stress-energy tensors constructed from the covariant
derivatives of delta functions on a worldline. Since covariant derivatives are
used all the components transform as tensors. We derive the dynamical equations
for the components, up to quadrupole order. The components do, however, depend
in a non-tensorial way, on a choice of a vector along the worldline. We also
derive a number of important results about general multipoles, including that
their components are unique, and all multipoles can be written using covariant
derivatives. We show how the components of a multipole are related to standard
moments of a tensor field, by parallelly transporting that tensor field.Comment: 27 pages, 2 figure